Abstract
State-space models (SSMs) are becoming mainstream for time series analysis because their flexibility and increased explainability, as they model observations separately from unobserved dynamics. Critically, using SSMs based on multivariate autoregressive equations enhances understanding of system evolution and its dynamical interactions. However, some challenges remain unsolved, such as estimation in large-scale scenarios, with very noisy data, and model selection. Here, we explore a state-space alternating least squares (SSALS) algorithm for time series forecasting, demonstrating its application with simulated and real data, and how to solve model selection in noisy scenarios with a novel cross-validation technique. Altogether, testing this methodology with time series forecasting is ideal to demonstrate its strengths and weaknesses, and appreciate its advantages compared to current methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
AugerMéthé, M., Newman, K., Cole, D., Empacher, F., Gryba, R., King, A., LeosBarajas, V., Mills Flemming, J., Nielsen, A., Petris, G., Thomas, L., "A guide to state-space modeling of ecological time series", 91(4) (2021)
Barnett, L., Seth, A.K.: The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference. J. Neurosci. Methods 223, 50–68 (2014)
Puthanmadam, S.N., Tronarp, F., Särkkä, S., Parkkonen, L., "Joint estimation of neural sources and their functional connections from MEG data". Preprint, 1–24, (2020). https://doi.org/10.1101/2020.10.04.325563
Van de Steen, F., Faes, L., Karahan, E., Songsiri, J., Valdes-Sosa, P., Marinazzo, D., "Critical Comments on EEG Sensor Space Dynamical Connectivity Analysis". Brain Topography, 643–654, 32(4) (2019). https://doi.org/10.1007/s10548-016-0538-7
Manomaisaowapak, P., Nartkulpat, A., Songsiri, J., "Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach". IEEE Transactions on Neural Networks and Learning Systems, 1–11 (2021)
Sanchez-Bornot, J.M., Sotero, R.C., Kelso S., Özgür Ş., Coyle, D., "Solving large-scale MEG/EEG source localization and functional connectivity problems simultaneously using state-space models". Submitted to Neuroimage (under major revision). Preprint: arxiv.org/abs/2208.12854v1 (2022)
Sanchez-Bornot, J.M., Sotero, R.C., Coyle, D., "Dynamic source localization and functional connectivity estimation with state-space models: preliminary feasibility analysis". In ICASSP 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2023). Poster and video. Matlab code.
Hastie, T., Friedman, J., Tibshirani, R., "The Elements of Statistical Learning". Springer Series in Statistics. Springer, New York (2001). https://doi.org/10.1007/978-0-387-21606-5,isbn: 978-1-4899-0519-2
Bergmeir, C., Hyndman, R.J., Koo, B.: A note on the validity of cross-validation for evaluating autoregressive time series prediction. Comput. Stat. Data Anal. 120, 70–83 (2018)
Bergmeir, C., Benítez, J.M.: On the use of cross-validation for time series predictor evaluation. Inf. Sci. 191, 192–213 (2012)
Varoquaux, G., et al.: Assessing and tuning brain decoders: cross-validation, caveats, and guidelines. Neuroimage 145, 166–179 (2017)
Li, X., Kang, Y., Li, F., "Forecasting with time series imaging". Expert Systems with Applications, 160 (2020)
Holmes, E., Ward, E.J., Wills, K., "MARSS : Multivariate Autoregressive State-space Models for Analyzing Time-series Data". R J. 4(1) (2012)
Langville, A.N., Meyer, C.D., Albright, R., Cox, J., Duling, D., "Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization". Preprint: arxiv.org/abs/1407.7299 (2014)
Acknowledgments
The authors are grateful for access to the Tier 2 High-Performance Computing resources provided by the Northern Ireland High Performance Computing (NI-HPC) facility funded by the UK Engineering and Physical Sciences Research Council (EPSRC), Grant No. EP/T022175/1. RCS was supported by RGPIN-2022-03042 from Natural Sciences and Engineering Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Sanchez-Bornot, J.M., Sotero, R.C. (2023). Machine Learning for Time Series Forecasting Using State Space Models. In: Quaresma, P., Camacho, D., Yin, H., Gonçalves, T., Julian, V., Tallón-Ballesteros, A.J. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2023. IDEAL 2023. Lecture Notes in Computer Science, vol 14404. Springer, Cham. https://doi.org/10.1007/978-3-031-48232-8_43
Download citation
DOI: https://doi.org/10.1007/978-3-031-48232-8_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-48231-1
Online ISBN: 978-3-031-48232-8
eBook Packages: Computer ScienceComputer Science (R0)